DIGITAL VERSION OF THE MATHERON REPRESENTATION THEOREM FOR INCREASING tau -MAPPINGS IN TERMS OF A BASIS FOR THE KERNEL. Conference Paper uri icon

abstract

  • G. Matheron (1975) has given a fundamental representation theorem for increasing tau -mappings. He shows that for Euclidean constant images (subsets of the plane) every increasing tau -mapping admits a representation in terms of a union of erosions over the kernel of the mapping. The proof of the theorem goes through without essential alteration for discrete constant images (subsets of the grid Z multiplied by Z). Through the introduction of a basis for the kernel, a practical finite representation result can be achieved for digital images with some restriction on the class over which the representation holds.

author list (cited authors)

  • Dougherty, E. R., & Giardina, C. R.

complete list of authors

  • Dougherty, ER||Giardina, CR

publication date

  • January 1986